"Special Parallelogram" PPT Courseware 2

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"Special Parallelogram" PPT Courseware 2

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Definition: A parallelogram with one right angle is called a rectangle.

1. It is a parallelogram

2. One angle is a right angle

A study of the properties of rectangles

We already know that a rectangle is a special parallelogram, so in addition to the properties of a parallelogram, a rectangle also has other special properties. Can you tell what special properties a rectangle has?

1. The two opposite sides of the rectangle are parallel

2. The two opposite sides of the rectangle are equal

3. The two opposite angles of the rectangle are equal

4. Rectangle Two diagonals bisect each other

5. The adjacent angles of a rectangle are complementary

A rectangle is a special parallelogram. In addition to having all the properties of a parallelogram, what other special properties does it have?

Conjecture 1: The four corners of the rectangle are all right angles.

Conjecture 2: The diagonals of the rectangle are equal.

Proposition 1: The four corners of a rectangle are right angles

Known: Quadrilateral ABCD is a rectangle, ∠B=90°

Prove: ∠A=∠B=∠C=∠D=90°

Prove: ∵ Quadrilateral ABCD is a parallelogram, ∠B=90°

∴∠B=∠D=90° ∠B+∠C=180 °

∴∠B+∠A=180°

∴∠A=∠B=∠C=∠D=90°

Proposition 2: The diagonals of rectangles are equal.

It is known that quadrilateral ABCD is a rectangle. Prove: AC = BD

Proof: In rectangle ABCD

∵∠ABC = ∠DCB = 90°

And ∵AB = DC, BC = CB

∴△ABC≌△DCB

∴AC = BD

Try your hand

Quadrilateral ABCD is a rectangle

1. If it is known that AB=8cm and AD=6cm,

Then AC=_______cm OB=_______ cm

2. If it is known that AC=10cm and BC=6cm, then the perimeter of the rectangle=____ cm

Area of ​​rectangle =_______cm2

3. If it is known that ∠DOC=120°, AD=6cm, then AC= _____cm

Pass practice:

1. The length of the two sides of the rectangle is 6 and 8, then the length of the diagonal of the rectangle is _________

2. The perimeter of a rectangle is 24cm, and the ratio of two adjacent sides is 1:3. Then the area of ​​this rectangle is _________

3. The angle between one diagonal of a rectangle and one side is 35°, then the acute angle formed by the intersection of the diagonals is___________

4. The length of the shorter side of the rectangle is 3.6cm, and the acute angle where the two diagonals intersect is 60°, then the length of the diagonal of the rectangle is __________

5. The side lengths of the rectangle are 45cm and 20cm. The bisector of one of the interior angles divides the longer side into two parts. The side length is __________

Improvement after class:

1. In the rectangle ABDC, CE⊥BD, the vertical foot is E. If ∠DCE=3∠ECB, find the degree of ∠ACE.

2. If the bisector of an interior angle of a rectangle divides one side of it into two parts of 3cm and 5cm, what is its area?

Example analysis:

Example 1: The two diagonals of the rectangle ABCD intersect at point 0, ∠AOD=120°, AB = 4cm, find the length of the diagonal of the rectangle.

Solution: ∵ Quadrilateral ABCD is a rectangle

∴AC = BD (the diagonals of the rectangle are equal)

∴OA=OC=1/2AC

OB= OD=1/2BD (the diagonals of the parallelogram bisect each other)

∴OA=OB

∵∠AOD=120°

∴∠AOB=180°－∠AOD = 60°

∴ △AOB is an equilateral triangle ∴OA=OB=AB=4cm

∴AC = 2OA=8cm.

life link

1. In order to celebrate May 1st Labor Day, the students in Grade 8 (13) of Xinmin School will arrange a rectangular flower bed in the square. They plan to use "strings of red" to form two diagonal lines. If one diagonal line uses 38 How many more pots of "Chun Hong" need to be transported from the greenhouse? Why? What if 49 pots are used on a diagonal? Why?

2. As shown in the figure, 8 identical rectangular floor tiles are used to form a rectangular floor. The length and width of each rectangular floor tile are ( )

(A) 48cm, 12cm; (B) 48cm, 16cm;

(C) 44cm, 16cm; (D) 45cm, 15cm.

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"Special Parallelograms" PPT courseware 6:

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"Special Parallelograms" PPT courseware 5:

"Special Parallelograms" PPT Courseware 5 Scenario Creation We have studied parallelograms and rectangles before, and we know what shape it will become if one of the angles of a parallelogram is a right angle? (A rectangle is obtained by changing the angle) If the parallelogram is transformed from the angle of the side special..

"Special Parallelogram" PPT Courseware 4:

"Special Parallelograms" PPT Courseware 4 Review Review Definition: A parallelogram with one right angle is called a rectangle. Give it a try. It is known that △ABC is Rt△, ABC=Rt, and BD is the midline on the hypotenuse AC. 1. If BD=3cm, then AC=________cm 2. If C=30, A..

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Update Time: 2024-09-09

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